Question

What is the inverse of function f? F(X) = square root of x +7

Answer 1

Answer: $f^{-1} (x)=x^{2} -7$

Step-by-step explanation:

To find the inverse of a function replace f(x) with x and the original x with y

$f(x)=\sqrt{x+7} \\x=\sqrt{y+7}$

Now we can solve for y

Square both sides so we can cancel out the root

$x=\sqrt{y+7}\\x^{2} =\sqrt{y+7}^{2} \\x^{2} =y+7$

Now subtract 7 from both sides

$x^{2} =y+7\\x^{2} -7=y+7-7\\x^{2} -7=y$

Now replace y with the inverse of f(x), $f^{-1} (x)$

Answer 2

Answer:

f⁻¹=x²+7

Solution:

• In order to find the inverse of a function, we should first replace f(x) with y, then switch x and y places, like so:
• y=√x+7
• x=√y+7
• Now, solve the equation for y.
• Square both sides in order to get rid of the square root:
• x²+7=y
• y=x²+7
• And finally, replace y with f⁻¹:
• f⁻¹=x²+7
• Also, inverse functions do the opposite thing in the opposite order.
• So if we have f(x)=x+7, the inverse function is: f⁻¹=x-7

Hope it helps.

Do comment if you have any query.